Hollow fiber bundles composed of intersecting hollow fibers extending essentially in the lengthwise direction of the hollow fiber bundle are sufficiently known (U.S. Pat. No. 4,346,006). Depending on the nature of the hollow fibers employed, they are used to transfer heat and/or material in the technical area, for example for reverse osmosis, ultra- or microfiltration, pervaporation, membrane distillation, etc., and also especially in the medical area, in which application they are used especially for treating blood, for example in dialysis, blood oxygenation, plasma separation, plasmapheresis, hemofiltration, blood heat exchangers, etc. The hollow fiber bundle according to the invention can also be used for all of these applications.